Heap size: 40 Array contents: ALGORITHMS-CAMBRIDGE-2015-HEAPSORT … · 2015-02-02 · Initially...

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Initially the array may not satisfy the heap property.The heap will be built up by calling heapify on all internal nodes from the bottom up.

Heap size: 40 Array contents: ALGORITHMS-CAMBRIDGE-2015-HEAPSORT-GS509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: - 11: C 12: A 13: M 14: B

15: R 16: I 17: D 18: G 19: E 20: - 21: 2 22: 0 23: 1 24: 5 25: - 26: H 27: E 28: A 29: P 30: S

31: O 32: R 33: T 34: - 35: G 36: S 37: 5 38: 0 39: 9

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Running heapify on node 19 as part of the build heap (heap-up) process.Heap size: 40 Array contents: ALGORITHMS-CAMBRIDGE-2015-HEAPSORT-GS509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: - 11: C 12: A 13: M 14: B

15: R 16: I 17: D 18: G 19: E 20: - 21: 2 22: 0 23: 1 24: 5 25: - 26: H 27: E 28: A 29: P 30: S

31: O 32: R 33: T 34: - 35: G 36: S 37: 5 38: 0 39: 9

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Largest of node 19 and its children is node 19.No swap is necessary, heapify done.

Heap size: 40 Array contents: ALGORITHMS-CAMBRIDGE-2015-HEAPSORT-GS509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: - 11: C 12: A 13: M 14: B

15: R 16: I 17: D 18: G 19: E 20: - 21: 2 22: 0 23: 1 24: 5 25: - 26: H 27: E 28: A 29: P 30: S

31: O 32: R 33: T 34: - 35: G 36: S 37: 5 38: 0 39: 9

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Running heapify on node 18 as part of the build heap (heap-up) process.Heap size: 40 Array contents: ALGORITHMS-CAMBRIDGE-2015-HEAPSORT-GS509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: - 11: C 12: A 13: M 14: B

15: R 16: I 17: D 18: G 19: E 20: - 21: 2 22: 0 23: 1 24: 5 25: - 26: H 27: E 28: A 29: P 30: S

31: O 32: R 33: T 34: - 35: G 36: S 37: 5 38: 0 39: 9

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Largest of node 18 and its children is node 18.No swap is necessary, heapify done.

Heap size: 40 Array contents: ALGORITHMS-CAMBRIDGE-2015-HEAPSORT-GS509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: - 11: C 12: A 13: M 14: B

15: R 16: I 17: D 18: G 19: E 20: - 21: 2 22: 0 23: 1 24: 5 25: - 26: H 27: E 28: A 29: P 30: S

31: O 32: R 33: T 34: - 35: G 36: S 37: 5 38: 0 39: 9

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Running heapify on node 17 as part of the build heap (heap-up) process.Heap size: 40 Array contents: ALGORITHMS-CAMBRIDGE-2015-HEAPSORT-GS509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: - 11: C 12: A 13: M 14: B

15: R 16: I 17: D 18: G 19: E 20: - 21: 2 22: 0 23: 1 24: 5 25: - 26: H 27: E 28: A 29: P 30: S

31: O 32: R 33: T 34: - 35: G 36: S 37: 5 38: 0 39: 9

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Largest of node 17 and its children is node 36.Root and max will be swapped and heapify will recurse on the new node 36.

Heap size: 40 Array contents: ALGORITHMS-CAMBRIDGE-2015-HEAPSORT-GS509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: - 11: C 12: A 13: M 14: B

15: R 16: I 17: D 18: G 19: E 20: - 21: 2 22: 0 23: 1 24: 5 25: - 26: H 27: E 28: A 29: P 30: S

31: O 32: R 33: T 34: - 35: G 36: S 37: 5 38: 0 39: 9

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Running heapify on node 36.Heap size: 40 Array contents: ALGORITHMS-CAMBRISGE-2015-HEAPSORT-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: - 11: C 12: A 13: M 14: B

15: R 16: I 17: S 18: G 19: E 20: - 21: 2 22: 0 23: 1 24: 5 25: - 26: H 27: E 28: A 29: P 30: S

31: O 32: R 33: T 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 36 and its children is node 36.No swap is necessary, heapify done.

Heap size: 40 Array contents: ALGORITHMS-CAMBRISGE-2015-HEAPSORT-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: - 11: C 12: A 13: M 14: B

15: R 16: I 17: S 18: G 19: E 20: - 21: 2 22: 0 23: 1 24: 5 25: - 26: H 27: E 28: A 29: P 30: S

31: O 32: R 33: T 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 16 as part of the build heap (heap-up) process.Heap size: 40 Array contents: ALGORITHMS-CAMBRISGE-2015-HEAPSORT-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: - 11: C 12: A 13: M 14: B

15: R 16: I 17: S 18: G 19: E 20: - 21: 2 22: 0 23: 1 24: 5 25: - 26: H 27: E 28: A 29: P 30: S

31: O 32: R 33: T 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 16 and its children is node 33.Root and max will be swapped and heapify will recurse on the new node 33.

Heap size: 40 Array contents: ALGORITHMS-CAMBRISGE-2015-HEAPSORT-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: - 11: C 12: A 13: M 14: B

15: R 16: I 17: S 18: G 19: E 20: - 21: 2 22: 0 23: 1 24: 5 25: - 26: H 27: E 28: A 29: P 30: S

31: O 32: R 33: T 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 33.Heap size: 40 Array contents: ALGORITHMS-CAMBRTSGE-2015-HEAPSORI-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: - 11: C 12: A 13: M 14: B

15: R 16: T 17: S 18: G 19: E 20: - 21: 2 22: 0 23: 1 24: 5 25: - 26: H 27: E 28: A 29: P 30: S

31: O 32: R 33: I 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 33 and its children is node 33.No swap is necessary, heapify done.

Heap size: 40 Array contents: ALGORITHMS-CAMBRTSGE-2015-HEAPSORI-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: - 11: C 12: A 13: M 14: B

15: R 16: T 17: S 18: G 19: E 20: - 21: 2 22: 0 23: 1 24: 5 25: - 26: H 27: E 28: A 29: P 30: S

31: O 32: R 33: I 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 15 as part of the build heap (heap-up) process.Heap size: 40 Array contents: ALGORITHMS-CAMBRTSGE-2015-HEAPSORI-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: - 11: C 12: A 13: M 14: B

15: R 16: T 17: S 18: G 19: E 20: - 21: 2 22: 0 23: 1 24: 5 25: - 26: H 27: E 28: A 29: P 30: S

31: O 32: R 33: I 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 15 and its children is node 15.No swap is necessary, heapify done.

Heap size: 40 Array contents: ALGORITHMS-CAMBRTSGE-2015-HEAPSORI-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: - 11: C 12: A 13: M 14: B

15: R 16: T 17: S 18: G 19: E 20: - 21: 2 22: 0 23: 1 24: 5 25: - 26: H 27: E 28: A 29: P 30: S

31: O 32: R 33: I 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 14 as part of the build heap (heap-up) process.Heap size: 40 Array contents: ALGORITHMS-CAMBRTSGE-2015-HEAPSORI-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: - 11: C 12: A 13: M 14: B

15: R 16: T 17: S 18: G 19: E 20: - 21: 2 22: 0 23: 1 24: 5 25: - 26: H 27: E 28: A 29: P 30: S

31: O 32: R 33: I 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 14 and its children is node 30.Root and max will be swapped and heapify will recurse on the new node 30.

Heap size: 40 Array contents: ALGORITHMS-CAMBRTSGE-2015-HEAPSORI-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: - 11: C 12: A 13: M 14: B

15: R 16: T 17: S 18: G 19: E 20: - 21: 2 22: 0 23: 1 24: 5 25: - 26: H 27: E 28: A 29: P 30: S

31: O 32: R 33: I 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 30.Heap size: 40 Array contents: ALGORITHMS-CAMSRTSGE-2015-HEAPBORI-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: - 11: C 12: A 13: M 14: S

15: R 16: T 17: S 18: G 19: E 20: - 21: 2 22: 0 23: 1 24: 5 25: - 26: H 27: E 28: A 29: P 30: B

31: O 32: R 33: I 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 30 and its children is node 30.No swap is necessary, heapify done.

Heap size: 40 Array contents: ALGORITHMS-CAMSRTSGE-2015-HEAPBORI-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: - 11: C 12: A 13: M 14: S

15: R 16: T 17: S 18: G 19: E 20: - 21: 2 22: 0 23: 1 24: 5 25: - 26: H 27: E 28: A 29: P 30: B

31: O 32: R 33: I 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 13 as part of the build heap (heap-up) process.Heap size: 40 Array contents: ALGORITHMS-CAMSRTSGE-2015-HEAPBORI-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: - 11: C 12: A 13: M 14: S

15: R 16: T 17: S 18: G 19: E 20: - 21: 2 22: 0 23: 1 24: 5 25: - 26: H 27: E 28: A 29: P 30: B

31: O 32: R 33: I 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 13 and its children is node 13.No swap is necessary, heapify done.

Heap size: 40 Array contents: ALGORITHMS-CAMSRTSGE-2015-HEAPBORI-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: - 11: C 12: A 13: M 14: S

15: R 16: T 17: S 18: G 19: E 20: - 21: 2 22: 0 23: 1 24: 5 25: - 26: H 27: E 28: A 29: P 30: B

31: O 32: R 33: I 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 12 as part of the build heap (heap-up) process.Heap size: 40 Array contents: ALGORITHMS-CAMSRTSGE-2015-HEAPBORI-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: - 11: C 12: A 13: M 14: S

15: R 16: T 17: S 18: G 19: E 20: - 21: 2 22: 0 23: 1 24: 5 25: - 26: H 27: E 28: A 29: P 30: B

31: O 32: R 33: I 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 12 and its children is node 26.Root and max will be swapped and heapify will recurse on the new node 26.

Heap size: 40 Array contents: ALGORITHMS-CAMSRTSGE-2015-HEAPBORI-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: - 11: C 12: A 13: M 14: S

15: R 16: T 17: S 18: G 19: E 20: - 21: 2 22: 0 23: 1 24: 5 25: - 26: H 27: E 28: A 29: P 30: B

31: O 32: R 33: I 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 26.Heap size: 40 Array contents: ALGORITHMS-CHMSRTSGE-2015-AEAPBORI-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: - 11: C 12: H 13: M 14: S

15: R 16: T 17: S 18: G 19: E 20: - 21: 2 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: I 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 26 and its children is node 26.No swap is necessary, heapify done.

Heap size: 40 Array contents: ALGORITHMS-CHMSRTSGE-2015-AEAPBORI-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: - 11: C 12: H 13: M 14: S

15: R 16: T 17: S 18: G 19: E 20: - 21: 2 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: I 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 11 as part of the build heap (heap-up) process.Heap size: 40 Array contents: ALGORITHMS-CHMSRTSGE-2015-AEAPBORI-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: - 11: C 12: H 13: M 14: S

15: R 16: T 17: S 18: G 19: E 20: - 21: 2 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: I 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 11 and its children is node 11.No swap is necessary, heapify done.

Heap size: 40 Array contents: ALGORITHMS-CHMSRTSGE-2015-AEAPBORI-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: - 11: C 12: H 13: M 14: S

15: R 16: T 17: S 18: G 19: E 20: - 21: 2 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: I 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 10 as part of the build heap (heap-up) process.Heap size: 40 Array contents: ALGORITHMS-CHMSRTSGE-2015-AEAPBORI-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: - 11: C 12: H 13: M 14: S

15: R 16: T 17: S 18: G 19: E 20: - 21: 2 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: I 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 10 and its children is node 21.Root and max will be swapped and heapify will recurse on the new node 21.

Heap size: 40 Array contents: ALGORITHMS-CHMSRTSGE-2015-AEAPBORI-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: - 11: C 12: H 13: M 14: S

15: R 16: T 17: S 18: G 19: E 20: - 21: 2 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: I 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 21.Heap size: 40 Array contents: ALGORITHMS2CHMSRTSGE--015-AEAPBORI-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: 2 11: C 12: H 13: M 14: S

15: R 16: T 17: S 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: I 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 21 and its children is node 21.No swap is necessary, heapify done.

Heap size: 40 Array contents: ALGORITHMS2CHMSRTSGE--015-AEAPBORI-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: 2 11: C 12: H 13: M 14: S

15: R 16: T 17: S 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: I 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 9 as part of the build heap (heap-up) process.Heap size: 40 Array contents: ALGORITHMS2CHMSRTSGE--015-AEAPBORI-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: 2 11: C 12: H 13: M 14: S

15: R 16: T 17: S 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: I 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 9 and its children is node 9.No swap is necessary, heapify done.

Heap size: 40 Array contents: ALGORITHMS2CHMSRTSGE--015-AEAPBORI-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: 2 11: C 12: H 13: M 14: S

15: R 16: T 17: S 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: I 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 8 as part of the build heap (heap-up) process.Heap size: 40 Array contents: ALGORITHMS2CHMSRTSGE--015-AEAPBORI-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: 2 11: C 12: H 13: M 14: S

15: R 16: T 17: S 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: I 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 8 and its children is node 17.Root and max will be swapped and heapify will recurse on the new node 17.

Heap size: 40 Array contents: ALGORITHMS2CHMSRTSGE--015-AEAPBORI-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: M 9: S 10: 2 11: C 12: H 13: M 14: S

15: R 16: T 17: S 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: I 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 17.Heap size: 40 Array contents: ALGORITHSS2CHMSRTMGE--015-AEAPBORI-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: S 9: S 10: 2 11: C 12: H 13: M 14: S

15: R 16: T 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: I 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 17 and its children is node 17.No swap is necessary, heapify done.

Heap size: 40 Array contents: ALGORITHSS2CHMSRTMGE--015-AEAPBORI-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: S 9: S 10: 2 11: C 12: H 13: M 14: S

15: R 16: T 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: I 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 7 as part of the build heap (heap-up) process.Heap size: 40 Array contents: ALGORITHSS2CHMSRTMGE--015-AEAPBORI-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: S 9: S 10: 2 11: C 12: H 13: M 14: S

15: R 16: T 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: I 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 7 and its children is node 16.Root and max will be swapped and heapify will recurse on the new node 16.

Heap size: 40 Array contents: ALGORITHSS2CHMSRTMGE--015-AEAPBORI-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: H 8: S 9: S 10: 2 11: C 12: H 13: M 14: S

15: R 16: T 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: I 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 16.Heap size: 40 Array contents: ALGORITTSS2CHMSRHMGE--015-AEAPBORI-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: T 8: S 9: S 10: 2 11: C 12: H 13: M 14: S

15: R 16: H 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: I 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 16 and its children is node 33.Root and max will be swapped and heapify will recurse on the new node 33.

Heap size: 40 Array contents: ALGORITTSS2CHMSRHMGE--015-AEAPBORI-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: T 8: S 9: S 10: 2 11: C 12: H 13: M 14: S

15: R 16: H 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: I 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 33.Heap size: 40 Array contents: ALGORITTSS2CHMSRIMGE--015-AEAPBORH-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: T 8: S 9: S 10: 2 11: C 12: H 13: M 14: S

15: R 16: I 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 33 and its children is node 33.No swap is necessary, heapify done.

Heap size: 40 Array contents: ALGORITTSS2CHMSRIMGE--015-AEAPBORH-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: T 8: S 9: S 10: 2 11: C 12: H 13: M 14: S

15: R 16: I 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 6 as part of the build heap (heap-up) process.Heap size: 40 Array contents: ALGORITTSS2CHMSRIMGE--015-AEAPBORH-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: T 8: S 9: S 10: 2 11: C 12: H 13: M 14: S

15: R 16: I 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 6 and its children is node 6.No swap is necessary, heapify done.

Heap size: 40 Array contents: ALGORITTSS2CHMSRIMGE--015-AEAPBORH-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: T 8: S 9: S 10: 2 11: C 12: H 13: M 14: S

15: R 16: I 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 5 as part of the build heap (heap-up) process.Heap size: 40 Array contents: ALGORITTSS2CHMSRIMGE--015-AEAPBORH-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: T 8: S 9: S 10: 2 11: C 12: H 13: M 14: S

15: R 16: I 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 5 and its children is node 5.No swap is necessary, heapify done.

Heap size: 40 Array contents: ALGORITTSS2CHMSRIMGE--015-AEAPBORH-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: T 8: S 9: S 10: 2 11: C 12: H 13: M 14: S

15: R 16: I 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 4 as part of the build heap (heap-up) process.Heap size: 40 Array contents: ALGORITTSS2CHMSRIMGE--015-AEAPBORH-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: T 8: S 9: S 10: 2 11: C 12: H 13: M 14: S

15: R 16: I 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 4 and its children is node 9.Root and max will be swapped and heapify will recurse on the new node 9.

Heap size: 40 Array contents: ALGORITTSS2CHMSRIMGE--015-AEAPBORH-GD509

0: A

1: L 2: G

3: O 4: R 5: I 6: T

7: T 8: S 9: S 10: 2 11: C 12: H 13: M 14: S

15: R 16: I 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 9.Heap size: 40 Array contents: ALGOSITTSR2CHMSRIMGE--015-AEAPBORH-GD509

0: A

1: L 2: G

3: O 4: S 5: I 6: T

7: T 8: S 9: R 10: 2 11: C 12: H 13: M 14: S

15: R 16: I 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 9 and its children is node 9.No swap is necessary, heapify done.

Heap size: 40 Array contents: ALGOSITTSR2CHMSRIMGE--015-AEAPBORH-GD509

0: A

1: L 2: G

3: O 4: S 5: I 6: T

7: T 8: S 9: R 10: 2 11: C 12: H 13: M 14: S

15: R 16: I 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 3 as part of the build heap (heap-up) process.Heap size: 40 Array contents: ALGOSITTSR2CHMSRIMGE--015-AEAPBORH-GD509

0: A

1: L 2: G

3: O 4: S 5: I 6: T

7: T 8: S 9: R 10: 2 11: C 12: H 13: M 14: S

15: R 16: I 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 3 and its children is node 7.Root and max will be swapped and heapify will recurse on the new node 7.

Heap size: 40 Array contents: ALGOSITTSR2CHMSRIMGE--015-AEAPBORH-GD509

0: A

1: L 2: G

3: O 4: S 5: I 6: T

7: T 8: S 9: R 10: 2 11: C 12: H 13: M 14: S

15: R 16: I 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 7.Heap size: 40 Array contents: ALGTSITOSR2CHMSRIMGE--015-AEAPBORH-GD509

0: A

1: L 2: G

3: T 4: S 5: I 6: T

7: O 8: S 9: R 10: 2 11: C 12: H 13: M 14: S

15: R 16: I 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 7 and its children is node 15.Root and max will be swapped and heapify will recurse on the new node 15.

Heap size: 40 Array contents: ALGTSITOSR2CHMSRIMGE--015-AEAPBORH-GD509

0: A

1: L 2: G

3: T 4: S 5: I 6: T

7: O 8: S 9: R 10: 2 11: C 12: H 13: M 14: S

15: R 16: I 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 15.Heap size: 40 Array contents: ALGTSITRSR2CHMSOIMGE--015-AEAPBORH-GD509

0: A

1: L 2: G

3: T 4: S 5: I 6: T

7: R 8: S 9: R 10: 2 11: C 12: H 13: M 14: S

15: O 16: I 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 15 and its children is node 32.Root and max will be swapped and heapify will recurse on the new node 32.

Heap size: 40 Array contents: ALGTSITRSR2CHMSOIMGE--015-AEAPBORH-GD509

0: A

1: L 2: G

3: T 4: S 5: I 6: T

7: R 8: S 9: R 10: 2 11: C 12: H 13: M 14: S

15: O 16: I 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: R 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 32.Heap size: 40 Array contents: ALGTSITRSR2CHMSRIMGE--015-AEAPBOOH-GD509

0: A

1: L 2: G

3: T 4: S 5: I 6: T

7: R 8: S 9: R 10: 2 11: C 12: H 13: M 14: S

15: R 16: I 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 32 and its children is node 32.No swap is necessary, heapify done.

Heap size: 40 Array contents: ALGTSITRSR2CHMSRIMGE--015-AEAPBOOH-GD509

0: A

1: L 2: G

3: T 4: S 5: I 6: T

7: R 8: S 9: R 10: 2 11: C 12: H 13: M 14: S

15: R 16: I 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 2 as part of the build heap (heap-up) process.Heap size: 40 Array contents: ALGTSITRSR2CHMSRIMGE--015-AEAPBOOH-GD509

0: A

1: L 2: G

3: T 4: S 5: I 6: T

7: R 8: S 9: R 10: 2 11: C 12: H 13: M 14: S

15: R 16: I 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 2 and its children is node 6.Root and max will be swapped and heapify will recurse on the new node 6.

Heap size: 40 Array contents: ALGTSITRSR2CHMSRIMGE--015-AEAPBOOH-GD509

0: A

1: L 2: G

3: T 4: S 5: I 6: T

7: R 8: S 9: R 10: 2 11: C 12: H 13: M 14: S

15: R 16: I 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 6.Heap size: 40 Array contents: ALTTSIGRSR2CHMSRIMGE--015-AEAPBOOH-GD509

0: A

1: L 2: T

3: T 4: S 5: I 6: G

7: R 8: S 9: R 10: 2 11: C 12: H 13: M 14: S

15: R 16: I 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 6 and its children is node 14.Root and max will be swapped and heapify will recurse on the new node 14.

Heap size: 40 Array contents: ALTTSIGRSR2CHMSRIMGE--015-AEAPBOOH-GD509

0: A

1: L 2: T

3: T 4: S 5: I 6: G

7: R 8: S 9: R 10: 2 11: C 12: H 13: M 14: S

15: R 16: I 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 14.Heap size: 40 Array contents: ALTTSISRSR2CHMGRIMGE--015-AEAPBOOH-GD509

0: A

1: L 2: T

3: T 4: S 5: I 6: S

7: R 8: S 9: R 10: 2 11: C 12: H 13: M 14: G

15: R 16: I 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 14 and its children is node 29.Root and max will be swapped and heapify will recurse on the new node 29.

Heap size: 40 Array contents: ALTTSISRSR2CHMGRIMGE--015-AEAPBOOH-GD509

0: A

1: L 2: T

3: T 4: S 5: I 6: S

7: R 8: S 9: R 10: 2 11: C 12: H 13: M 14: G

15: R 16: I 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: P 30: B

31: O 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 29.Heap size: 40 Array contents: ALTTSISRSR2CHMPRIMGE--015-AEAGBOOH-GD509

0: A

1: L 2: T

3: T 4: S 5: I 6: S

7: R 8: S 9: R 10: 2 11: C 12: H 13: M 14: P

15: R 16: I 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: G 30: B

31: O 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 29 and its children is node 29.No swap is necessary, heapify done.

Heap size: 40 Array contents: ALTTSISRSR2CHMPRIMGE--015-AEAGBOOH-GD509

0: A

1: L 2: T

3: T 4: S 5: I 6: S

7: R 8: S 9: R 10: 2 11: C 12: H 13: M 14: P

15: R 16: I 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: G 30: B

31: O 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 1 as part of the build heap (heap-up) process.Heap size: 40 Array contents: ALTTSISRSR2CHMPRIMGE--015-AEAGBOOH-GD509

0: A

1: L 2: T

3: T 4: S 5: I 6: S

7: R 8: S 9: R 10: 2 11: C 12: H 13: M 14: P

15: R 16: I 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: G 30: B

31: O 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 1 and its children is node 3.Root and max will be swapped and heapify will recurse on the new node 3.

Heap size: 40 Array contents: ALTTSISRSR2CHMPRIMGE--015-AEAGBOOH-GD509

0: A

1: L 2: T

3: T 4: S 5: I 6: S

7: R 8: S 9: R 10: 2 11: C 12: H 13: M 14: P

15: R 16: I 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: G 30: B

31: O 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 3.Heap size: 40 Array contents: ATTLSISRSR2CHMPRIMGE--015-AEAGBOOH-GD509

0: A

1: T 2: T

3: L 4: S 5: I 6: S

7: R 8: S 9: R 10: 2 11: C 12: H 13: M 14: P

15: R 16: I 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: G 30: B

31: O 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 3 and its children is node 8.Root and max will be swapped and heapify will recurse on the new node 8.

Heap size: 40 Array contents: ATTLSISRSR2CHMPRIMGE--015-AEAGBOOH-GD509

0: A

1: T 2: T

3: L 4: S 5: I 6: S

7: R 8: S 9: R 10: 2 11: C 12: H 13: M 14: P

15: R 16: I 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: G 30: B

31: O 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 8.Heap size: 40 Array contents: ATTSSISRLR2CHMPRIMGE--015-AEAGBOOH-GD509

0: A

1: T 2: T

3: S 4: S 5: I 6: S

7: R 8: L 9: R 10: 2 11: C 12: H 13: M 14: P

15: R 16: I 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: G 30: B

31: O 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 8 and its children is node 17.Root and max will be swapped and heapify will recurse on the new node 17.

Heap size: 40 Array contents: ATTSSISRLR2CHMPRIMGE--015-AEAGBOOH-GD509

0: A

1: T 2: T

3: S 4: S 5: I 6: S

7: R 8: L 9: R 10: 2 11: C 12: H 13: M 14: P

15: R 16: I 17: M 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: G 30: B

31: O 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 17.Heap size: 40 Array contents: ATTSSISRMR2CHMPRILGE--015-AEAGBOOH-GD509

0: A

1: T 2: T

3: S 4: S 5: I 6: S

7: R 8: M 9: R 10: 2 11: C 12: H 13: M 14: P

15: R 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: G 30: B

31: O 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 17 and its children is node 17.No swap is necessary, heapify done.

Heap size: 40 Array contents: ATTSSISRMR2CHMPRILGE--015-AEAGBOOH-GD509

0: A

1: T 2: T

3: S 4: S 5: I 6: S

7: R 8: M 9: R 10: 2 11: C 12: H 13: M 14: P

15: R 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: G 30: B

31: O 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 0 as part of the build heap (heap-up) process.Heap size: 40 Array contents: ATTSSISRMR2CHMPRILGE--015-AEAGBOOH-GD509

0: A

1: T 2: T

3: S 4: S 5: I 6: S

7: R 8: M 9: R 10: 2 11: C 12: H 13: M 14: P

15: R 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: G 30: B

31: O 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 0 and its children is node 1.Root and max will be swapped and heapify will recurse on the new node 1.

Heap size: 40 Array contents: ATTSSISRMR2CHMPRILGE--015-AEAGBOOH-GD509

0: A

1: T 2: T

3: S 4: S 5: I 6: S

7: R 8: M 9: R 10: 2 11: C 12: H 13: M 14: P

15: R 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: G 30: B

31: O 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 1.Heap size: 40 Array contents: TATSSISRMR2CHMPRILGE--015-AEAGBOOH-GD509

0: T

1: A 2: T

3: S 4: S 5: I 6: S

7: R 8: M 9: R 10: 2 11: C 12: H 13: M 14: P

15: R 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: G 30: B

31: O 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 1 and its children is node 3.Root and max will be swapped and heapify will recurse on the new node 3.

Heap size: 40 Array contents: TATSSISRMR2CHMPRILGE--015-AEAGBOOH-GD509

0: T

1: A 2: T

3: S 4: S 5: I 6: S

7: R 8: M 9: R 10: 2 11: C 12: H 13: M 14: P

15: R 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: G 30: B

31: O 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 3.Heap size: 40 Array contents: TSTASISRMR2CHMPRILGE--015-AEAGBOOH-GD509

0: T

1: S 2: T

3: A 4: S 5: I 6: S

7: R 8: M 9: R 10: 2 11: C 12: H 13: M 14: P

15: R 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: G 30: B

31: O 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 3 and its children is node 7.Root and max will be swapped and heapify will recurse on the new node 7.

Heap size: 40 Array contents: TSTASISRMR2CHMPRILGE--015-AEAGBOOH-GD509

0: T

1: S 2: T

3: A 4: S 5: I 6: S

7: R 8: M 9: R 10: 2 11: C 12: H 13: M 14: P

15: R 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: G 30: B

31: O 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 7.Heap size: 40 Array contents: TSTRSISAMR2CHMPRILGE--015-AEAGBOOH-GD509

0: T

1: S 2: T

3: R 4: S 5: I 6: S

7: A 8: M 9: R 10: 2 11: C 12: H 13: M 14: P

15: R 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: G 30: B

31: O 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 7 and its children is node 15.Root and max will be swapped and heapify will recurse on the new node 15.

Heap size: 40 Array contents: TSTRSISAMR2CHMPRILGE--015-AEAGBOOH-GD509

0: T

1: S 2: T

3: R 4: S 5: I 6: S

7: A 8: M 9: R 10: 2 11: C 12: H 13: M 14: P

15: R 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: G 30: B

31: O 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 15.Heap size: 40 Array contents: TSTRSISRMR2CHMPAILGE--015-AEAGBOOH-GD509

0: T

1: S 2: T

3: R 4: S 5: I 6: S

7: R 8: M 9: R 10: 2 11: C 12: H 13: M 14: P

15: A 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: G 30: B

31: O 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 15 and its children is node 31.Root and max will be swapped and heapify will recurse on the new node 31.

Heap size: 40 Array contents: TSTRSISRMR2CHMPAILGE--015-AEAGBOOH-GD509

0: T

1: S 2: T

3: R 4: S 5: I 6: S

7: R 8: M 9: R 10: 2 11: C 12: H 13: M 14: P

15: A 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: G 30: B

31: O 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 31.Heap size: 40 Array contents: TSTRSISRMR2CHMPOILGE--015-AEAGBAOH-GD509

0: T

1: S 2: T

3: R 4: S 5: I 6: S

7: R 8: M 9: R 10: 2 11: C 12: H 13: M 14: P

15: O 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: G 30: B

31: A 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Largest of node 31 and its children is node 31.No swap is necessary, heapify done.

Heap size: 40 Array contents: TSTRSISRMR2CHMPOILGE--015-AEAGBAOH-GD509

0: T

1: S 2: T

3: R 4: S 5: I 6: S

7: R 8: M 9: R 10: 2 11: C 12: H 13: M 14: P

15: O 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: G 30: B

31: A 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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The array now satisfies the heap property.The heap will be emptied by repeatedly taking the root element

and moving it outside of the heap in the underlying array.Heap size: 40 Array contents: TSTRSISRMR2CHMPOILGE--015-AEAGBAOH-GD509

0: T

1: S 2: T

3: R 4: S 5: I 6: S

7: R 8: M 9: R 10: 2 11: C 12: H 13: M 14: P

15: O 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: G 30: B

31: A 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Removing root and moving it outside of the heap.The last element takes its place and the heap size is decremented.

Heap size: 40 Array contents: TSTRSISRMR2CHMPOILGE--015-AEAGBAOH-GD509

0: T

1: S 2: T

3: R 4: S 5: I 6: S

7: R 8: M 9: R 10: 2 11: C 12: H 13: M 14: P

15: O 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: G 30: B

31: A 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0 39: 9

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Running heapify on node 0 as part of the repair heap (heap-down) process.Heap size: 39 Array contents: 9STRSISRMR2CHMPOILGE--015-AEAGBAOH-GD50T

0: 9

1: S 2: T

3: R 4: S 5: I 6: S

7: R 8: M 9: R 10: 2 11: C 12: H 13: M 14: P

15: O 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: G 30: B

31: A 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0

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Largest of node 0 and its children is node 2.Root and max will be swapped and heapify will recurse on the new node 2.

Heap size: 39 Array contents: 9STRSISRMR2CHMPOILGE--015-AEAGBAOH-GD50T

0: 9

1: S 2: T

3: R 4: S 5: I 6: S

7: R 8: M 9: R 10: 2 11: C 12: H 13: M 14: P

15: O 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: G 30: B

31: A 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0

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Running heapify on node 2.Heap size: 39 Array contents: TS9RSISRMR2CHMPOILGE--015-AEAGBAOH-GD50T

0: T

1: S 2: 9

3: R 4: S 5: I 6: S

7: R 8: M 9: R 10: 2 11: C 12: H 13: M 14: P

15: O 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: G 30: B

31: A 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0

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Largest of node 2 and its children is node 6.Root and max will be swapped and heapify will recurse on the new node 6.

Heap size: 39 Array contents: TS9RSISRMR2CHMPOILGE--015-AEAGBAOH-GD50T

0: T

1: S 2: 9

3: R 4: S 5: I 6: S

7: R 8: M 9: R 10: 2 11: C 12: H 13: M 14: P

15: O 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: G 30: B

31: A 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0

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Running heapify on node 6.Heap size: 39 Array contents: TSSRSI9RMR2CHMPOILGE--015-AEAGBAOH-GD50T

0: T

1: S 2: S

3: R 4: S 5: I 6: 9

7: R 8: M 9: R 10: 2 11: C 12: H 13: M 14: P

15: O 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: G 30: B

31: A 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0

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Largest of node 6 and its children is node 14.Root and max will be swapped and heapify will recurse on the new node 14.

Heap size: 39 Array contents: TSSRSI9RMR2CHMPOILGE--015-AEAGBAOH-GD50T

0: T

1: S 2: S

3: R 4: S 5: I 6: 9

7: R 8: M 9: R 10: 2 11: C 12: H 13: M 14: P

15: O 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: G 30: B

31: A 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0

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Running heapify on node 14.Heap size: 39 Array contents: TSSRSIPRMR2CHM9OILGE--015-AEAGBAOH-GD50T

0: T

1: S 2: S

3: R 4: S 5: I 6: P

7: R 8: M 9: R 10: 2 11: C 12: H 13: M 14: 9

15: O 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: G 30: B

31: A 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0

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Largest of node 14 and its children is node 29.Root and max will be swapped and heapify will recurse on the new node 29.

Heap size: 39 Array contents: TSSRSIPRMR2CHM9OILGE--015-AEAGBAOH-GD50T

0: T

1: S 2: S

3: R 4: S 5: I 6: P

7: R 8: M 9: R 10: 2 11: C 12: H 13: M 14: 9

15: O 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: G 30: B

31: A 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0

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Running heapify on node 29.Heap size: 39 Array contents: TSSRSIPRMR2CHMGOILGE--015-AEA9BAOH-GD50T

0: T

1: S 2: S

3: R 4: S 5: I 6: P

7: R 8: M 9: R 10: 2 11: C 12: H 13: M 14: G

15: O 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0

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Largest of node 29 and its children is node 29.No swap is necessary, heapify done.

Heap size: 39 Array contents: TSSRSIPRMR2CHMGOILGE--015-AEA9BAOH-GD50T

0: T

1: S 2: S

3: R 4: S 5: I 6: P

7: R 8: M 9: R 10: 2 11: C 12: H 13: M 14: G

15: O 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0

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Removing root and moving it outside of the heap.The last element takes its place and the heap size is decremented.

Heap size: 39 Array contents: TSSRSIPRMR2CHMGOILGE--015-AEA9BAOH-GD50T

0: T

1: S 2: S

3: R 4: S 5: I 6: P

7: R 8: M 9: R 10: 2 11: C 12: H 13: M 14: G

15: O 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: O 33: H 34: - 35: G 36: D 37: 5 38: 0

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Running heapify on node 0 as part of the repair heap (heap-down) process.Heap size: 38 Array contents: 0SSRSIPRMR2CHMGOILGE--015-AEA9BAOH-GD5TT

0: 0

1: S 2: S

3: R 4: S 5: I 6: P

7: R 8: M 9: R 10: 2 11: C 12: H 13: M 14: G

15: O 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: O 33: H 34: - 35: G 36: D 37: 5

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Largest of node 0 and its children is node 1.Root and max will be swapped and heapify will recurse on the new node 1.

Heap size: 38 Array contents: 0SSRSIPRMR2CHMGOILGE--015-AEA9BAOH-GD5TT

0: 0

1: S 2: S

3: R 4: S 5: I 6: P

7: R 8: M 9: R 10: 2 11: C 12: H 13: M 14: G

15: O 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: O 33: H 34: - 35: G 36: D 37: 5

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Running heapify on node 1.Heap size: 38 Array contents: S0SRSIPRMR2CHMGOILGE--015-AEA9BAOH-GD5TT

0: S

1: 0 2: S

3: R 4: S 5: I 6: P

7: R 8: M 9: R 10: 2 11: C 12: H 13: M 14: G

15: O 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: O 33: H 34: - 35: G 36: D 37: 5

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Largest of node 1 and its children is node 4.Root and max will be swapped and heapify will recurse on the new node 4.

Heap size: 38 Array contents: S0SRSIPRMR2CHMGOILGE--015-AEA9BAOH-GD5TT

0: S

1: 0 2: S

3: R 4: S 5: I 6: P

7: R 8: M 9: R 10: 2 11: C 12: H 13: M 14: G

15: O 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: O 33: H 34: - 35: G 36: D 37: 5

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Running heapify on node 4.Heap size: 38 Array contents: SSSR0IPRMR2CHMGOILGE--015-AEA9BAOH-GD5TT

0: S

1: S 2: S

3: R 4: 0 5: I 6: P

7: R 8: M 9: R 10: 2 11: C 12: H 13: M 14: G

15: O 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: O 33: H 34: - 35: G 36: D 37: 5

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Largest of node 4 and its children is node 9.Root and max will be swapped and heapify will recurse on the new node 9.

Heap size: 38 Array contents: SSSR0IPRMR2CHMGOILGE--015-AEA9BAOH-GD5TT

0: S

1: S 2: S

3: R 4: 0 5: I 6: P

7: R 8: M 9: R 10: 2 11: C 12: H 13: M 14: G

15: O 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: O 33: H 34: - 35: G 36: D 37: 5

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Running heapify on node 9.Heap size: 38 Array contents: SSSRRIPRM02CHMGOILGE--015-AEA9BAOH-GD5TT

0: S

1: S 2: S

3: R 4: R 5: I 6: P

7: R 8: M 9: 0 10: 2 11: C 12: H 13: M 14: G

15: O 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: O 33: H 34: - 35: G 36: D 37: 5

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Largest of node 9 and its children is node 19.Root and max will be swapped and heapify will recurse on the new node 19.

Heap size: 38 Array contents: SSSRRIPRM02CHMGOILGE--015-AEA9BAOH-GD5TT

0: S

1: S 2: S

3: R 4: R 5: I 6: P

7: R 8: M 9: 0 10: 2 11: C 12: H 13: M 14: G

15: O 16: I 17: L 18: G 19: E 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: O 33: H 34: - 35: G 36: D 37: 5

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Running heapify on node 19.Heap size: 38 Array contents: SSSRRIPRME2CHMGOILG0--015-AEA9BAOH-GD5TT

0: S

1: S 2: S

3: R 4: R 5: I 6: P

7: R 8: M 9: E 10: 2 11: C 12: H 13: M 14: G

15: O 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: O 33: H 34: - 35: G 36: D 37: 5

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Largest of node 19 and its children is node 19.No swap is necessary, heapify done.

Heap size: 38 Array contents: SSSRRIPRME2CHMGOILG0--015-AEA9BAOH-GD5TT

0: S

1: S 2: S

3: R 4: R 5: I 6: P

7: R 8: M 9: E 10: 2 11: C 12: H 13: M 14: G

15: O 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: O 33: H 34: - 35: G 36: D 37: 5

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Removing root and moving it outside of the heap.The last element takes its place and the heap size is decremented.

Heap size: 38 Array contents: SSSRRIPRME2CHMGOILG0--015-AEA9BAOH-GD5TT

0: S

1: S 2: S

3: R 4: R 5: I 6: P

7: R 8: M 9: E 10: 2 11: C 12: H 13: M 14: G

15: O 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: O 33: H 34: - 35: G 36: D 37: 5

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Running heapify on node 0 as part of the repair heap (heap-down) process.Heap size: 37 Array contents: 5SSRRIPRME2CHMGOILG0--015-AEA9BAOH-GDSTT

0: 5

1: S 2: S

3: R 4: R 5: I 6: P

7: R 8: M 9: E 10: 2 11: C 12: H 13: M 14: G

15: O 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: O 33: H 34: - 35: G 36: D

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Largest of node 0 and its children is node 1.Root and max will be swapped and heapify will recurse on the new node 1.

Heap size: 37 Array contents: 5SSRRIPRME2CHMGOILG0--015-AEA9BAOH-GDSTT

0: 5

1: S 2: S

3: R 4: R 5: I 6: P

7: R 8: M 9: E 10: 2 11: C 12: H 13: M 14: G

15: O 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: O 33: H 34: - 35: G 36: D

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Running heapify on node 1.Heap size: 37 Array contents: S5SRRIPRME2CHMGOILG0--015-AEA9BAOH-GDSTT

0: S

1: 5 2: S

3: R 4: R 5: I 6: P

7: R 8: M 9: E 10: 2 11: C 12: H 13: M 14: G

15: O 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: O 33: H 34: - 35: G 36: D

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Largest of node 1 and its children is node 3.Root and max will be swapped and heapify will recurse on the new node 3.

Heap size: 37 Array contents: S5SRRIPRME2CHMGOILG0--015-AEA9BAOH-GDSTT

0: S

1: 5 2: S

3: R 4: R 5: I 6: P

7: R 8: M 9: E 10: 2 11: C 12: H 13: M 14: G

15: O 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: O 33: H 34: - 35: G 36: D

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Running heapify on node 3.Heap size: 37 Array contents: SRS5RIPRME2CHMGOILG0--015-AEA9BAOH-GDSTT

0: S

1: R 2: S

3: 5 4: R 5: I 6: P

7: R 8: M 9: E 10: 2 11: C 12: H 13: M 14: G

15: O 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: O 33: H 34: - 35: G 36: D

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Largest of node 3 and its children is node 7.Root and max will be swapped and heapify will recurse on the new node 7.

Heap size: 37 Array contents: SRS5RIPRME2CHMGOILG0--015-AEA9BAOH-GDSTT

0: S

1: R 2: S

3: 5 4: R 5: I 6: P

7: R 8: M 9: E 10: 2 11: C 12: H 13: M 14: G

15: O 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: O 33: H 34: - 35: G 36: D

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Running heapify on node 7.Heap size: 37 Array contents: SRSRRIP5ME2CHMGOILG0--015-AEA9BAOH-GDSTT

0: S

1: R 2: S

3: R 4: R 5: I 6: P

7: 5 8: M 9: E 10: 2 11: C 12: H 13: M 14: G

15: O 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: O 33: H 34: - 35: G 36: D

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Largest of node 7 and its children is node 15.Root and max will be swapped and heapify will recurse on the new node 15.

Heap size: 37 Array contents: SRSRRIP5ME2CHMGOILG0--015-AEA9BAOH-GDSTT

0: S

1: R 2: S

3: R 4: R 5: I 6: P

7: 5 8: M 9: E 10: 2 11: C 12: H 13: M 14: G

15: O 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: O 33: H 34: - 35: G 36: D

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Running heapify on node 15.Heap size: 37 Array contents: SRSRRIPOME2CHMG5ILG0--015-AEA9BAOH-GDSTT

0: S

1: R 2: S

3: R 4: R 5: I 6: P

7: O 8: M 9: E 10: 2 11: C 12: H 13: M 14: G

15: 5 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: O 33: H 34: - 35: G 36: D

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Largest of node 15 and its children is node 32.Root and max will be swapped and heapify will recurse on the new node 32.

Heap size: 37 Array contents: SRSRRIPOME2CHMG5ILG0--015-AEA9BAOH-GDSTT

0: S

1: R 2: S

3: R 4: R 5: I 6: P

7: O 8: M 9: E 10: 2 11: C 12: H 13: M 14: G

15: 5 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: O 33: H 34: - 35: G 36: D

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Running heapify on node 32.Heap size: 37 Array contents: SRSRRIPOME2CHMGOILG0--015-AEA9BA5H-GDSTT

0: S

1: R 2: S

3: R 4: R 5: I 6: P

7: O 8: M 9: E 10: 2 11: C 12: H 13: M 14: G

15: O 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: 5 33: H 34: - 35: G 36: D

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Largest of node 32 and its children is node 32.No swap is necessary, heapify done.

Heap size: 37 Array contents: SRSRRIPOME2CHMGOILG0--015-AEA9BA5H-GDSTT

0: S

1: R 2: S

3: R 4: R 5: I 6: P

7: O 8: M 9: E 10: 2 11: C 12: H 13: M 14: G

15: O 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: 5 33: H 34: - 35: G 36: D

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Removing root and moving it outside of the heap.The last element takes its place and the heap size is decremented.

Heap size: 37 Array contents: SRSRRIPOME2CHMGOILG0--015-AEA9BA5H-GDSTT

0: S

1: R 2: S

3: R 4: R 5: I 6: P

7: O 8: M 9: E 10: 2 11: C 12: H 13: M 14: G

15: O 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: 5 33: H 34: - 35: G 36: D

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Running heapify on node 0 as part of the repair heap (heap-down) process.Heap size: 36 Array contents: DRSRRIPOME2CHMGOILG0--015-AEA9BA5H-GSSTT

0: D

1: R 2: S

3: R 4: R 5: I 6: P

7: O 8: M 9: E 10: 2 11: C 12: H 13: M 14: G

15: O 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: 5 33: H 34: - 35: G

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Largest of node 0 and its children is node 2.Root and max will be swapped and heapify will recurse on the new node 2.

Heap size: 36 Array contents: DRSRRIPOME2CHMGOILG0--015-AEA9BA5H-GSSTT

0: D

1: R 2: S

3: R 4: R 5: I 6: P

7: O 8: M 9: E 10: 2 11: C 12: H 13: M 14: G

15: O 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: 5 33: H 34: - 35: G

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Running heapify on node 2.Heap size: 36 Array contents: SRDRRIPOME2CHMGOILG0--015-AEA9BA5H-GSSTT

0: S

1: R 2: D

3: R 4: R 5: I 6: P

7: O 8: M 9: E 10: 2 11: C 12: H 13: M 14: G

15: O 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: 5 33: H 34: - 35: G

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Largest of node 2 and its children is node 6.Root and max will be swapped and heapify will recurse on the new node 6.

Heap size: 36 Array contents: SRDRRIPOME2CHMGOILG0--015-AEA9BA5H-GSSTT

0: S

1: R 2: D

3: R 4: R 5: I 6: P

7: O 8: M 9: E 10: 2 11: C 12: H 13: M 14: G

15: O 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: 5 33: H 34: - 35: G

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Running heapify on node 6.Heap size: 36 Array contents: SRPRRIDOME2CHMGOILG0--015-AEA9BA5H-GSSTT

0: S

1: R 2: P

3: R 4: R 5: I 6: D

7: O 8: M 9: E 10: 2 11: C 12: H 13: M 14: G

15: O 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: 5 33: H 34: - 35: G

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Largest of node 6 and its children is node 13.Root and max will be swapped and heapify will recurse on the new node 13.

Heap size: 36 Array contents: SRPRRIDOME2CHMGOILG0--015-AEA9BA5H-GSSTT

0: S

1: R 2: P

3: R 4: R 5: I 6: D

7: O 8: M 9: E 10: 2 11: C 12: H 13: M 14: G

15: O 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: 5 33: H 34: - 35: G

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Running heapify on node 13.Heap size: 36 Array contents: SRPRRIMOME2CHDGOILG0--015-AEA9BA5H-GSSTT

0: S

1: R 2: P

3: R 4: R 5: I 6: M

7: O 8: M 9: E 10: 2 11: C 12: H 13: D 14: G

15: O 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: 5 33: H 34: - 35: G

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Largest of node 13 and its children is node 27.Root and max will be swapped and heapify will recurse on the new node 27.

Heap size: 36 Array contents: SRPRRIMOME2CHDGOILG0--015-AEA9BA5H-GSSTT

0: S

1: R 2: P

3: R 4: R 5: I 6: M

7: O 8: M 9: E 10: 2 11: C 12: H 13: D 14: G

15: O 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: E 28: A 29: 9 30: B

31: A 32: 5 33: H 34: - 35: G

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Running heapify on node 27.Heap size: 36 Array contents: SRPRRIMOME2CHEGOILG0--015-ADA9BA5H-GSSTT

0: S

1: R 2: P

3: R 4: R 5: I 6: M

7: O 8: M 9: E 10: 2 11: C 12: H 13: E 14: G

15: O 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: D 28: A 29: 9 30: B

31: A 32: 5 33: H 34: - 35: G

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Largest of node 27 and its children is node 27.No swap is necessary, heapify done.

Heap size: 36 Array contents: SRPRRIMOME2CHEGOILG0--015-ADA9BA5H-GSSTT

0: S

1: R 2: P

3: R 4: R 5: I 6: M

7: O 8: M 9: E 10: 2 11: C 12: H 13: E 14: G

15: O 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: D 28: A 29: 9 30: B

31: A 32: 5 33: H 34: - 35: G

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Removing root and moving it outside of the heap.The last element takes its place and the heap size is decremented.

Heap size: 36 Array contents: SRPRRIMOME2CHEGOILG0--015-ADA9BA5H-GSSTT

0: S

1: R 2: P

3: R 4: R 5: I 6: M

7: O 8: M 9: E 10: 2 11: C 12: H 13: E 14: G

15: O 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: D 28: A 29: 9 30: B

31: A 32: 5 33: H 34: - 35: G

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Running heapify on node 0 as part of the repair heap (heap-down) process.Heap size: 35 Array contents: GRPRRIMOME2CHEGOILG0--015-ADA9BA5H-SSSTT

0: G

1: R 2: P

3: R 4: R 5: I 6: M

7: O 8: M 9: E 10: 2 11: C 12: H 13: E 14: G

15: O 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: D 28: A 29: 9 30: B

31: A 32: 5 33: H 34: -

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Largest of node 0 and its children is node 1.Root and max will be swapped and heapify will recurse on the new node 1.

Heap size: 35 Array contents: GRPRRIMOME2CHEGOILG0--015-ADA9BA5H-SSSTT

0: G

1: R 2: P

3: R 4: R 5: I 6: M

7: O 8: M 9: E 10: 2 11: C 12: H 13: E 14: G

15: O 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: D 28: A 29: 9 30: B

31: A 32: 5 33: H 34: -

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Running heapify on node 1.Heap size: 35 Array contents: RGPRRIMOME2CHEGOILG0--015-ADA9BA5H-SSSTT

0: R

1: G 2: P

3: R 4: R 5: I 6: M

7: O 8: M 9: E 10: 2 11: C 12: H 13: E 14: G

15: O 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: D 28: A 29: 9 30: B

31: A 32: 5 33: H 34: -

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Largest of node 1 and its children is node 3.Root and max will be swapped and heapify will recurse on the new node 3.

Heap size: 35 Array contents: RGPRRIMOME2CHEGOILG0--015-ADA9BA5H-SSSTT

0: R

1: G 2: P

3: R 4: R 5: I 6: M

7: O 8: M 9: E 10: 2 11: C 12: H 13: E 14: G

15: O 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: D 28: A 29: 9 30: B

31: A 32: 5 33: H 34: -

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Running heapify on node 3.Heap size: 35 Array contents: RRPGRIMOME2CHEGOILG0--015-ADA9BA5H-SSSTT

0: R

1: R 2: P

3: G 4: R 5: I 6: M

7: O 8: M 9: E 10: 2 11: C 12: H 13: E 14: G

15: O 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: D 28: A 29: 9 30: B

31: A 32: 5 33: H 34: -

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Largest of node 3 and its children is node 7.Root and max will be swapped and heapify will recurse on the new node 7.

Heap size: 35 Array contents: RRPGRIMOME2CHEGOILG0--015-ADA9BA5H-SSSTT

0: R

1: R 2: P

3: G 4: R 5: I 6: M

7: O 8: M 9: E 10: 2 11: C 12: H 13: E 14: G

15: O 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: D 28: A 29: 9 30: B

31: A 32: 5 33: H 34: -

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Running heapify on node 7.Heap size: 35 Array contents: RRPORIMGME2CHEGOILG0--015-ADA9BA5H-SSSTT

0: R

1: R 2: P

3: O 4: R 5: I 6: M

7: G 8: M 9: E 10: 2 11: C 12: H 13: E 14: G

15: O 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: D 28: A 29: 9 30: B

31: A 32: 5 33: H 34: -

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Largest of node 7 and its children is node 15.Root and max will be swapped and heapify will recurse on the new node 15.

Heap size: 35 Array contents: RRPORIMGME2CHEGOILG0--015-ADA9BA5H-SSSTT

0: R

1: R 2: P

3: O 4: R 5: I 6: M

7: G 8: M 9: E 10: 2 11: C 12: H 13: E 14: G

15: O 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: D 28: A 29: 9 30: B

31: A 32: 5 33: H 34: -

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Running heapify on node 15.Heap size: 35 Array contents: RRPORIMOME2CHEGGILG0--015-ADA9BA5H-SSSTT

0: R

1: R 2: P

3: O 4: R 5: I 6: M

7: O 8: M 9: E 10: 2 11: C 12: H 13: E 14: G

15: G 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: D 28: A 29: 9 30: B

31: A 32: 5 33: H 34: -

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Largest of node 15 and its children is node 15.No swap is necessary, heapify done.

Heap size: 35 Array contents: RRPORIMOME2CHEGGILG0--015-ADA9BA5H-SSSTT

0: R

1: R 2: P

3: O 4: R 5: I 6: M

7: O 8: M 9: E 10: 2 11: C 12: H 13: E 14: G

15: G 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: D 28: A 29: 9 30: B

31: A 32: 5 33: H 34: -

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Removing root and moving it outside of the heap.The last element takes its place and the heap size is decremented.

Heap size: 35 Array contents: RRPORIMOME2CHEGGILG0--015-ADA9BA5H-SSSTT

0: R

1: R 2: P

3: O 4: R 5: I 6: M

7: O 8: M 9: E 10: 2 11: C 12: H 13: E 14: G

15: G 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: D 28: A 29: 9 30: B

31: A 32: 5 33: H 34: -

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Running heapify on node 0 as part of the repair heap (heap-down) process.Heap size: 34 Array contents: -RPORIMOME2CHEGGILG0--015-ADA9BA5HRSSSTT

0: -

1: R 2: P

3: O 4: R 5: I 6: M

7: O 8: M 9: E 10: 2 11: C 12: H 13: E 14: G

15: G 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: D 28: A 29: 9 30: B

31: A 32: 5 33: H

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Largest of node 0 and its children is node 1.Root and max will be swapped and heapify will recurse on the new node 1.

Heap size: 34 Array contents: -RPORIMOME2CHEGGILG0--015-ADA9BA5HRSSSTT

0: -

1: R 2: P

3: O 4: R 5: I 6: M

7: O 8: M 9: E 10: 2 11: C 12: H 13: E 14: G

15: G 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: D 28: A 29: 9 30: B

31: A 32: 5 33: H

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Running heapify on node 1.Heap size: 34 Array contents: R-PORIMOME2CHEGGILG0--015-ADA9BA5HRSSSTT

0: R

1: - 2: P

3: O 4: R 5: I 6: M

7: O 8: M 9: E 10: 2 11: C 12: H 13: E 14: G

15: G 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: D 28: A 29: 9 30: B

31: A 32: 5 33: H

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Largest of node 1 and its children is node 4.Root and max will be swapped and heapify will recurse on the new node 4.

Heap size: 34 Array contents: R-PORIMOME2CHEGGILG0--015-ADA9BA5HRSSSTT

0: R

1: - 2: P

3: O 4: R 5: I 6: M

7: O 8: M 9: E 10: 2 11: C 12: H 13: E 14: G

15: G 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: D 28: A 29: 9 30: B

31: A 32: 5 33: H

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Running heapify on node 4.Heap size: 34 Array contents: RRPO-IMOME2CHEGGILG0--015-ADA9BA5HRSSSTT

0: R

1: R 2: P

3: O 4: - 5: I 6: M

7: O 8: M 9: E 10: 2 11: C 12: H 13: E 14: G

15: G 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: D 28: A 29: 9 30: B

31: A 32: 5 33: H

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Largest of node 4 and its children is node 9.Root and max will be swapped and heapify will recurse on the new node 9.

Heap size: 34 Array contents: RRPO-IMOME2CHEGGILG0--015-ADA9BA5HRSSSTT

0: R

1: R 2: P

3: O 4: - 5: I 6: M

7: O 8: M 9: E 10: 2 11: C 12: H 13: E 14: G

15: G 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: D 28: A 29: 9 30: B

31: A 32: 5 33: H

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Running heapify on node 9.Heap size: 34 Array contents: RRPOEIMOM-2CHEGGILG0--015-ADA9BA5HRSSSTT

0: R

1: R 2: P

3: O 4: E 5: I 6: M

7: O 8: M 9: - 10: 2 11: C 12: H 13: E 14: G

15: G 16: I 17: L 18: G 19: 0 20: - 21: - 22: 0 23: 1 24: 5 25: - 26: A 27: D 28: A 29: 9 30: B

31: A 32: 5 33: H

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